Mantissa-preserving operations and robust algorithm based fault tolerance for matrix computations

A system-level method for achieving fault tolerance called algorithm-based fault tolerance (ABFT) has been proposed by a number of researchers. Many ABFT schemes use a floating-point checksum test to detect computation errors resulting from hardware faults. This makes the tests susceptible to roundo...

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Bibliographic Details
Published in:IEEE transactions on computers 1996-04, Vol.45 (4), p.408-424
Main Authors: Dutt, S., Assaad, F.T.
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer errors
Computer science
control theory
systems
Computer Society
Computer systems performance. Reliability
Error correction
Exact sciences and technology
Fault detection
Fault tolerance
Fault tolerant systems
Matrix decomposition
Robustness
Roundoff errors
Software
System testing
Theoretical computing
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Summary:A system-level method for achieving fault tolerance called algorithm-based fault tolerance (ABFT) has been proposed by a number of researchers. Many ABFT schemes use a floating-point checksum test to detect computation errors resulting from hardware faults. This makes the tests susceptible to roundoff inaccuracies in floating-point operations, which either cause false alarms or lead to undetected errors. Thresholding of the equality test has been commonly used to avoid false alarms; however, a good threshold that minimizes false alarms without reducing the error coverage significantly is difficult to find, especially when not much is known about the input data. Furthermore, thresholded checksums will inevitably miss lower-bit errors, which can get magnified as a computation such as LU decomposition progresses. We develop a theory for applying integer mantissa checksum tests to "mantissa-preserving" floating-point computations. This test is not susceptible to roundoff problems and yields 100% error coverage without false alarms. For computations that are not fully mantissa-preserving, we show how to apply the mantissa checksum test to the mantissa-preserving components of the computation and the floating-point test to the rest of the computation. We apply this general methodology to matrix-matrix multiplication and LU decomposition (using the Gaussian elimination (GE) algorithm), and find that the accuracy of this new "hybrid" testing scheme is substantially higher than the floating-point test with thresholding.
ISSN:0018-9340
1557-9956
DOI:10.1109/12.494099